Normally, with a healthy capacitor one millimeter gap shouldn't be a problem. (EDIT: Now, that statement might give a too important role for the capacitor when it comes to prevent a spark to jump a fixed distance gap, whats matter is the voltage.) The voltage in the primary coil is comparative low, I think some 100-300 volt and not much amperage so it has a hard time jumping one millimetre of gap.
When the points break, the current from the primary tries to keep flowing because of the self induction. That ionizes the air gap between the points, resulting in a conductive arc. With the capacitor across the gap, the primary coil unloads in the time it takes to charge the capacitor, in about 60 millionths of a second, supressing the arc effectively, and the main goal is to stop the primary current flow as fast as possible. So the points doesn't open much before the primary is emptied. I use a thin paper between the points to set time of breaking. And before the current has build up again in the coil because of resonance, the points have had time to open enough to prevent a spark to form again.
That doesn't mean you couldn't have problem with that small distance to the oil tube, vibrations might short the points out randomly.
A sidenote. Primary coil inductance, magnet strength, engine max speed, in short how much energy the primary can contain is calculated and determine the size of the capacitor in mF. The coil and capacitor resonate with each other at a particular rate dictated in part by the capacitance in the capacitor. Too small capacitor and the current will spill over and arc between the points, too big and the charging of the capacitor is incomplete, too slow, resulting in low voltage in the secondary coil and that also changes the time the plug fires.
The points need to open much more than the paper thickness, partly because coil voltage (electrons) is bouncing back and forth between the capacitor and coil and an arc can build up later in the sequense, and there is also the risk of the points bouncing that can fire a plug randomly.
A second sidenote, there is a safety gap inside the magneto that is located in parallel with the coil secondary circuit. When secondary resistance becomes very high, such as when one of the spark plug wires is disconnected, the safety gap whose gap is much wider than a spark-plug gap, conducts the current to ground. This prevents breakdown of the highly-insulated magneto components.
